FEM analysis of binary dilute system solidification using the anisotropic porous medium model of a mushy zone

• Autorzy: Banaszek J. , Furmański P.
• Języki publikacji: EN

Abstrakty

EN

Finite Element Method (FEM) calculations have been performed to address the problem of the influence of anisotropy of permeability and of thermal conductivity of a mushy region on a temporary flow pattern and temperature during solidification of binary mixtures. Computationally effective FEM algorithm is based on the combination of the projection method, the semi-implicit time marching scheme and the enthalpy-porosity model of the two-phase region. Example calculations are given for two different dilute solutions of ammonium chloride and water. The effect of permeability anisotropy considerably changes the shape of the mushy zone. Three different models of thermal conductivity, the first - based on a mixture theory, the second - fully anisotropic one and the third - the model of isotropic effective conductivity, have been analyzed and mutually compared. It has been found that the impact of the thermal conductivity anisotropy is visible only in the case when this property differs significantly in both phases.

Słowa kluczowe

EN

finite element method; anisotropy; solidification; porous medium

PL

metoda elementów skończonych; anizotropia; krzepnięcie; czynnik porowaty

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Computer Assisted Mechanics and Engineering Sciences
• Rocznik: 2000
• Tom: Vol. 7, No. 3
• Strony: 341--362
• Opis fizyczny: Bibliogr. 27 poz., rys., tab., wykr.

Twórcy

autor

Banaszek J.

• Politechnika Warszawska, Instytut Techniki Cieplnej, ul. Nowowiejska 25, 00-665 Warszawa, Polska

autor

Furmański P.

• Politechnika Warszawska, Instytut Techniki Cieplnej, ul. Nowowiejska 25, 00-665 Warszawa, Polska

Bibliografia

• [1] G. A. Amhalhel, P. Furmański. Problems of modeling of flow and heat transfer in porous media. Bulletin of Institute of Heat Engineering, 85: 55-88, 1997.
• [2] J. Banaszek, Y. Jaluria, T. A. Kowalewski, M. Rebow. Semi-implicit FEM analysis of natural convection in freezing water. Numerical Heat Transfer, Part A., 36: 449-472, 1999.
• [3] W. D. Bennon, F. P. Incropera. A continuum model for momentum, heat and spieces transoprt in binary solidliquid phase change systems - I. Model formulation. Int. J. Heat Mass Transfer, 30: 2161-2170, 1987.
• [4] W. D. Bennon, F. P. Incropera. A continuum model for momentum, heat and spieces transoprt in binary solidliquid phase change systems - II. Application to solidification in a rectangular cavity. Int. J. Heat Mass Transfer, 30: 2171-2187, 1987.
• [5] A. D. Brent, V. R. Voller, K. J. Reid. Enthalpy-porosity technique for modeling convection diffusion phase change: application to the melting of pure metal. Numerical Heat Transfer, 13: 297-318, 1988.
• [6] J. Chorin. Numerical solution of Navier-Stokes equations. Math. Comp., 22: 745-762, 1968.
• [7] S. D. Felicelli, J. C. Heinrich, D. R. Poirier. Numerical model for dendritic solidification of binary alloys. Numerical Heat Transfer, Part B, 23: 461-481, 1993.
• [8] M. C. Flemings. Solidification Processing. McGraw-Hill, New York, 1974.
• [9] P. Furmański. Heat conduction in composites: homogenization and macroscopic behavior. Applied Mechanics Reviews, 50: 327-356, 1997.
• [10] B. Gebhart, Y. Jaluria, R. L. Mahajan, B. Sammakia. Buoyancy Induced Flows and Transport. Hemisphere Publishing Corporation, New York, 1988.
• [11] P. M. Gresho. On the theory of semi-implicit projection methods for viscous incompressible flow and its implementation via a finite element method that also introduces a nearly consistent mass matrix. Part 1: Theory. Numerical Heat Transfer, Part A, 29: 49-63, 1996.
• [12] International Critical Tables of Numerical Data, Physics, Chemistry and Technology. 3, 4. National Research Council U.S., McGraw-Hill, New York, 1933.
• [13] K. Kamiuto, S. Saitoh. Combined forced-convection and correlated-radiation heat transfer in cylindrical patches beds. J. Therrnophysics and Heat Transfer, 8: 119-124, 1994.
• [14] A. Mitrowski, P. Furmański. Numerical analysis of forced convection heat transfer during fully developed flow in a channel filled with porous medium. Archives of Thermodynamics, 19: 39-57, 1998.
• [15] G. F. Naterer, G. E. Schneider. Phases model for binary-constituent solid-liquid phase transition. Part 1: Numerical method. Numerical Heat Transfer, Part B, 28: 111-126, 1995.
• [16] D. R. Poirier. Permeability for flow of interdendritic liquid in columnar-dendritic alloys. Metallurgical Transactions B, 18B: 245-255, 1987
• [17] C. Prakash, V. R. Voller. On the numerical solution of continuum mixture model equations describing binary solid-liquid phase change. Numerical Heat Transfer, Part B, 15: 171-189, 1989.
• [18] B. Ramaswamy, T. C. Jue, J. E. Akin. Semi-implicit and explicit finite element schemes for coupled fluid/thermal problems. Int. J. Num. Meth. Eng., 34: 675-692, 1992.
• [19] S. K. Sinha, T. Sundarajan. A variable property analysis of alloy solidification using the anisotropic porous medium approach. Int. J. Heat Mass Transfer, 35: 2865-2877, 1992.
• [20] C. R. Swaminathan, V. R. Voller. General enthalpy method for modeling solidification processes. Metallurgical Transactions B, 23B: 651-664, 1992.
• [21] C. Taylor, T. J. R. Hughes. Finite Element Programming of the Navier-Stokes Equations. Pineridge Press, Swansea, 1981.
• [22] S. Usmani, R. W. Lewis, K. N. Seetharamu. Finite element modelling of 'natural convection-controlled change phase. Int. J. Num. Meth. in Fluids, 14: 1019-1036, 1992.
• [23] V. R. Voller, A. D. Brent, C. Prakash. The modeling of heat, mass and solute transport in solidification systems. Int. J. Heat Mass Transfer, 32: 1719-1731, 1989.
• [24] V. R. Voller, M. Cross, N. C. Markatos. An enthalpy method for convection/diffusion phase change. Int. J. Nu Meth. Eng., 24: 271-284, 1987.
• [25] V. R. Voller, C. Prakash. A fixed grid numerical modeling methodology for convection—diffusion mushy region phase-change problems. Int. J. Heat and Mass Transfer, 30: 1709-1719, 1987.
• [26] X. Zeng, A. Faghri. Temperature transforming model for binary solid—liquid phase-change problems. Part I Mathematical modeling and numerical methodology, Part II: Numerical simulation. Numerical Heat Transf er, Part B, 25: 467-480 and 481-500, 1993.
• [27] O. C. Zienkiewicz and R.L. Taylor. Finite element method. Fourth Edition, McGraw—Hill, London, 1989.